Orientational Order in fcc Solid Ortho-H2: Effect of the Spin-Lattice Coupling

The technique of temperature-dependent Green's functions, as applied in a previous paper, to a molecular-field model of the ordering of ortho-${\mathrm{H}}_2$ molecules on a rigid face-centered-cubic molecular lattice, is extended to include the effects of the interaction between the rotational motions of the molecules and the lattice vibrations on both the nature of the order-disorder transition and the value of the transition temperature for face-centered-cubic solid ortho-hydrogen. This "spin-lattice" coupling, resulting from the anisotropic van der Waals forces, is taken to be of the form proposed for hexagonal close-packed hydrogen. This interaction is found to lead to an additional, temperature-independent splitting of the $J=1\mathrm{}$ rotational level. Depending on the sign and magnitude of this splitting, it is shown that either a first-order, a second-order, or no transition is obtained.